Related papers: Families of prudent self-avoiding walks

We present two classes of random walks restricted to the quarter plane whose generating function is not holonomic. The non-holonomy is established using the iterated kernel method, a recent variant of the kernel method. This adds evidence…

We first study a model, introduced recently in \cite{ES}, of a critical branching random walk in an IID random environment on the $d$-dimensional integer lattice. The walker performs critical (0-2) branching at a lattice point if and only…

We review the existence of the infinite length self-avoiding walk in the half plane and its relationship to bridges. We prove that this probability measure is also given by the limit as $\beta \rightarrow \beta_c-$ of the probability…

The conjecture that the scaling limit of the two-dimensional self-avoiding walk (SAW) in a half plane is given by the stochastic Loewner evolution (SLE) with $\kappa=8/3$ leads to explicit predictions about the SAW. A remarkable feature of…

Different kinds of random walks have proven to be useful in the study of structural properties of complex networks. Among them, the restricted dynamics of self-avoiding random walks (SAW), which visit only at most once each vertex in the…

We study a discrete time self interacting random process on graphs, which we call Greedy Random Walk. The walker is located initially at some vertex. As time evolves, each vertex maintains the set of adjacent edges touching it that have not…

We recently published [J. Phys A: Math. Theor. {\bf 45} 115202 (2012)] a new and more efficient implementation of a transfer-matrix algorithm for exact enumerations of self-avoiding polygons. Here we extend this work to the enumeration of…

In a 1976 paper published in Science, Knuth presented an algorithm to sample (non-uniform) self-avoiding walks crossing a square of side k. From this sample, he constructed an estimator for the number of such walks. The quality of this…

Consider a single walker on the slit plane, that is, the square grid Z^2 without its negative x-axis, who starts at the origin and takes his steps from a given set S. Mireille Bousquet-Melou conjectured that -- excluding pathological cases…

We introduce branching annihilating attracting walk (BAAW) in one dimension. The attracting walk is implemented by a biased hopping in such a way that a particle prefers hopping to a nearest neighbor located on the side where the nearest…

We introduce a new class of models for polymer collapse, given by random walks on regular lattices which are weighted according to multiple site visits. A Boltzmann weight $\omega_l$ is assigned to each $(l+1)$-fold visited lattice site,…

A new family of discrete-time quantum walks (DTQWs) propagating on a regular $(1+2)$D spacetime lattice is introduced. The continuous limit of these DTQWs is shown to coincide with the dynamics of a Dirac fermion interacting with an…

In the present paper, we use difference Galois theory to study the nature of the generating function counting walks with small steps in the quarter plane. These series are trivariate formal power series $Q(x,y,t)$ that count the number of…

In the field of enumeration of weighted walks confined to the quarter plane, it is known that the generating functions behave very differently depending on the chosen step set; in practice, the techniques used in the literature depend on…

In order to study long chain polymers many lattice models accommodate a pulling force applied to a particular part of the chain, often a free endpoint. This is in addition to well-studied features such as energetic interaction between the…

We consider self-avoiding walks (SAWs) on the backbone of percolation clusters in space dimensions d=2, 3, 4. Applying numerical simulations, we show that the whole multifractal spectrum of singularities emerges in exploring the…

A rotor-router walk on a graph is a deterministic process, in which each vertex is endowed with a rotor that points to one of the neighbors. A particle located at some vertex first rotates the rotor in a prescribed order, and then it is…

We investigate neighbor-avoiding walks on the simple cubic lattice in the presence of an adsorbing surface. This class of lattice paths has been less studied using Monte Carlo simulations. Our investigation follows on from our previous…

Recently Beaton, de Gier and Guttmann proved a conjecture of Batchelor and Yung that the critical fugacity of self-avoiding walks interacting with (alternate) sites on the surface of the honeycomb lattice is $1+\sqrt{2}$. A key identity…

Let $G$ be a quasi-transitive, locally finite, connected graph rooted at a vertex $o$, and let $c_n(o)$ be the number of self-avoiding walks of length $n$ on $G$ starting at $o$. We show that if $G$ has only thin ends, then the generating…